US20220009044A1 - Method for manufacturing gear - Google Patents

Method for manufacturing gear Download PDF

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Publication number
US20220009044A1
US20220009044A1 US17/345,748 US202117345748A US2022009044A1 US 20220009044 A1 US20220009044 A1 US 20220009044A1 US 202117345748 A US202117345748 A US 202117345748A US 2022009044 A1 US2022009044 A1 US 2022009044A1
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United States
Prior art keywords
tooth
radius
function
tip
curvature
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Abandoned
Application number
US17/345,748
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English (en)
Inventor
Noriaki Yoshihiro
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Toyota Motor Corp
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Toyota Motor Corp
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Filing date
Publication date
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Assigned to TOYOTA JIDOSHA KABUSHIKI KAISHA reassignment TOYOTA JIDOSHA KABUSHIKI KAISHA ASSIGNMENT OF ASSIGNORS INTEREST (SEE DOCUMENT FOR DETAILS). Assignors: YOSHIHIRO, NORIAKI
Publication of US20220009044A1 publication Critical patent/US20220009044A1/en
Abandoned legal-status Critical Current

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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
    • B23P—METAL-WORKING NOT OTHERWISE PROVIDED FOR; COMBINED OPERATIONS; UNIVERSAL MACHINE TOOLS
    • B23P15/00—Making specific metal objects by operations not covered by a single other subclass or a group in this subclass
    • B23P15/14—Making specific metal objects by operations not covered by a single other subclass or a group in this subclass gear parts, e.g. gear wheels
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16H—GEARING
    • F16H55/00—Elements with teeth or friction surfaces for conveying motion; Worms, pulleys or sheaves for gearing mechanisms
    • F16H55/02—Toothed members; Worms
    • F16H55/08—Profiling
    • F16H55/0806—Involute profile
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/17—Mechanical parametric or variational design
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16H—GEARING
    • F16H55/00—Elements with teeth or friction surfaces for conveying motion; Worms, pulleys or sheaves for gearing mechanisms
    • F16H55/02—Toothed members; Worms
    • F16H55/08—Profiling
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q10/00—Administration; Management
    • G06Q10/06—Resources, workflows, human or project management; Enterprise or organisation planning; Enterprise or organisation modelling
    • G06Q10/063—Operations research, analysis or management
    • G06Q10/0635—Risk analysis of enterprise or organisation activities
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q50/00—Information and communication technology [ICT] specially adapted for implementation of business processes of specific business sectors, e.g. utilities or tourism
    • G06Q50/04—Manufacturing
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
    • B23F—MAKING GEARS OR TOOTHED RACKS
    • B23F17/00—Special methods or machines for making gear teeth, not covered by the preceding groups
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/10—Numerical modelling
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/18—Manufacturability analysis or optimisation for manufacturability

Definitions

  • the present disclosure relates to a method for manufacturing a gear.
  • Patent Literature 1 discloses a method for manufacturing a tooth part of a drive spindle for driving a roll of a rolling mill or the like.
  • a step of processing the tooth root of the arched tooth part so that it is lowered and a step of processing the tooth tip thereof so that it is lowered are performed separately.
  • Patent Literature 1 since the processing of a tooth part is divided into a plurality of steps, a precision error is more likely to occur than when the tooth part is processed in just one step. Meanwhile, forming a tooth profile by a quadratic function causes a problem that it is difficult to achieve both reduction of the risk of a collision of tooth tips and quietness.
  • the present disclosure has been made to solve the above-described problem and an object thereof is to provide a method for manufacturing a gear which is capable of reducing the risk of occurrence of a precision error in a tooth profile and achieving both reduction of the risk of a collision of tooth tips and quietness.
  • a first exemplary aspect is a method for manufacturing a gear, the method including: setting a function f(x) for forming a predetermined tooth profile in a gear, the function f(x) being defined so that: a surface shape of the tooth profile from a tooth root to a tooth tip has a vertex; a difference between a radius of curvature of the surface shape of the tooth profile at the tooth root and a radius of an arc or a radius of curvature of a parabola at the tooth root is within a predetermined value, the radius of the arc or the radius of curvature of the parabola at the tooth root being in contact with the vertex; a difference between a radius of curvature of the surface shape of the tooth profile at the tooth tip and the radius of the arc or a radius of curvature of the parabola at the tooth tip is equal to or greater than a predetermined value; and the radius of curvature of the surface shape of the tooth profile at the tooth tip becomes smaller than the radius of the arc or the
  • FIG. 1 is a diagram showing a gear according to an embodiment
  • FIG. 2 is a diagram showing an example of a function f(x) used to process a tooth profile in a method for manufacturing a gear according to the embodiment
  • FIG. 3 is a diagram for explaining another example of the function f(x) used to process the tooth profile in the method for manufacturing a gear according to the embodiment;
  • FIG. 5 is a diagram showing a function used to correct a tooth profile according to a comparative example
  • FIG. 6 is a diagram showing a function used to correct the tooth profile according to the comparative example.
  • FIG. 7 is a diagram showing a function used to correct the tooth profile according to the comparative example.
  • FIG. 1 is a diagram showing structures of gears 10 and 20 according to the embodiment.
  • the gears 10 and 20 have substantially disk-like shapes and have a plurality of teeth 11 and 21 on the outer circumferential side thereof, respectively.
  • FIG. 1 shows a state in which the gears 10 and 20 are engaged with each other at a position surrounded by a broken line circle.
  • the first shape is an involute curve, which is an ideal shape that achieves an ideal engagement when the gear is completely rigid and there is no assembly error.
  • the tooth 11 having the tooth flank 12 having an involute curve is formed into a symmetrical standard gear tooth profile 13 .
  • the second shape is a corrected shape obtained by taking the quietness and the smoothness of engagement into consideration based on a shape error and an assembling error.
  • the tooth tip and the side surface of a gear causes interference with a mating gear or puts high surface pressure on the mating gear, and thus wear occurs.
  • the respective teeth 11 and 21 are deformed by a load and hence a deflection occurs in a direction indicated by an arrow in FIG. 1 .
  • local wear occurs in the tooth width direction on the respective side surfaces of the teeth 11 and 21 .
  • the tooth tip of the gear 20 when the tooth flanks of the teeth that are to be engaged with each other next are not in the phase in which they are originally engaged, the tooth tip of the gear 20 , for example, interferes with the tooth root of the gear 10 or puts a high surface pressure (contact stress) on the tooth root of the gear 10 , and local wear of the teeth results. Engagement in which wear has occurred impairs quietness and the lifetime of the tooth tip and, in the worst case, a risk of causing destruction of the tooth tip arises.
  • a tooth tip relief shape obtained by correcting the tooth profile of a standard gear
  • the actual shape of the tooth profile is a geometric shape formed by combining an ideal shape and a corrected shape, and the corrected shape will be described below.
  • FIGS. 5, 6, and 7 show functions used to correct the tooth profile 13 of the gear according to the comparative example. In each of FIGS. 5 to 7 , the left side thereof is the tooth root side and the right side thereof is the tooth tip side.
  • the horizontal axis indicates a length of the line of action of the gear.
  • the length of the line of action is equal to a tooth height h shown in FIG. 1 .
  • the vertical axis indicates the position of the surface of the tooth flank.
  • the zero line of the vertical axis is an ideal shape of the surface shape of the tooth profile, and by using this zero line as a reference, processing of scraping the surface from the standard tooth profile as the surface shape of the tooth profile goes toward the minus side is performed.
  • a parabolic shape, an arc shape, and the like can be used as a corrected shape of the tooth shape which takes quietness into careful consideration.
  • a parabolic shape As a corrected shape of the tooth shape which takes quietness into careful consideration, a parabolic shape, an arc shape, and the like can be used.
  • FIGS. 5 and 6 an example of a parabolic shape is shown, and the parabola is expressed by the following Expression (1).
  • the surface shape of the tooth profile from the tooth root to the tooth tip has a vertex.
  • a point of contact between the vertex and an ideal shape is defined as O.
  • v is an end of the tooth tip side
  • ⁇ u(v>u) is an end of the tooth root side.
  • u is located between the vertex and the tooth tip.
  • c is an arbitrary proportional constant. By changing c, it is possible to change the shape of the tooth profile. Further, c shown in FIG. 5 is smaller than c shown in FIG. 6 .
  • a tooth profile having a high level of quietness can be designed by reducing c, a risk of interference of the tooth tips is high.
  • the risk of interference of the tooth tips can be reduced by increasing c, the level of the quietness is deteriorated due to a large deviation at the center of the tooth profile.
  • the tooth profile is divided into two regions to form a parabolic shape and a tooth tip relief shape which take quietness and interference of the tooth tips into consideration.
  • the parabolic shape of from A to B will achieve quietness and the tooth tip relief shape of from A to R will reduce a risk of interference of the tooth tips.
  • a point of discontinuity occurs at the point A.
  • NC numerical control
  • a method for manufacturing a gear includes: setting a function f(x) for forming a predetermined tooth profile in a gear, the function f(x) being defined so that: a surface shape of the tooth profile from a tooth root to a tooth tip has a vertex; a difference between a radius of curvature of the surface shape of the tooth profile at the tooth root and a radius of an arc or a radius of curvature of a parabola at the tooth root is within a predetermined value, the radius of the arc or the radius of curvature of the parabola at the tooth root being in contact with the vertex; a difference between a radius of curvature of the surface shape of the tooth profile at the tooth tip and the radius of the arc or a radius of curvature of the parabola at the tooth tip is equal to or greater than a predetermined value; and the radius
  • the above function f(x) is one general-purpose expression in which the surface shape of the tooth profile from the tooth root to the tooth tip becomes continuous and smooth. An example of the function f(x) will be described below.
  • FIG. 2 is a diagram showing the example of the function f(x) used to process a tooth profile in the method for manufacturing a gear according to the embodiment.
  • the function f(x) shown in FIG. 2 is expressed by the following Expression (2).
  • Expression (2) is an even function polynomial.
  • a parabola having the point O as a vertex is indicated by a broken line.
  • the surface shape of the tooth profile indicated by Expression (2) and the parabola indicated by the broken line are in contact with each other at the vertex (the point O).
  • Expression (2) when Expression (2) is used, the surface shape (from B to R via O and A) of the tooth profile from the tooth root to the tooth tip becomes continuous and smooth.
  • FIG. 3 is a diagram for explaining another example of the function f(x) used to process a tooth profile in the method for manufacturing a gear according to the embodiment.
  • the function f(x) shown in FIG. 2 is expressed by the following Expression (6).
  • Expression (6) is an even function exponential function expression.
  • a is determined from c, r, u, and v, and is equal to or greater than one.
  • the initial value of a is set to a 0 (S 1 ). Then a first derivative by a of g(a) shown in S 2 is obtained (S 3 ). Then an error ⁇ g of g(a) with respect to ⁇ is obtained (S 4 ). If the absolute value of ⁇ g is smaller than a tolerance ⁇ (yes in S 5 ), the calculation ends. On the other hand, if the absolute value of ⁇ g is equal to or greater than the tolerance ⁇ (no in S 5 ), Aa shown in S 6 is added to a, to thereby perform approximate correction on a (S 7 ), and the calculation is repeated for the approximate value until the absolute value of the error ⁇ g becomes smaller than the tolerance ⁇ .
  • the function f(x) in which the shape of the tooth root becomes a shape similar to the parabolic shape represented by a quadratic function and the shape of the tooth tip becomes a more curved shape than that of the parabolic shape.
  • the present disclosure is not limited to the above-described embodiment and may be modified as appropriate without departing from the spirit of the present disclosure.
  • the function f(x) according to the embodiment is compared with a parabola passing through the same vertex, it may instead be compared with an arc passing through the same vertex.
  • the above-described embodiment provides an example in which in NC machining, operations of a grinding tool, such as a grinding wheel, and a workpiece which is to be a gear are controlled to thereby form a predetermined tooth profile, but the present disclosure is not limited thereto.
  • a grinding tool such as a grinding wheel
  • a workpiece which is to be a gear is grounded with a grinding wheel to thereby finish the predetermined tooth shape
  • the grinding wheel can be dressed into a shape corresponding to the predetermined tooth shape by using the function f(x) described above.
  • the rolling die may be formed into a transfer shape corresponding to a predetermined tooth shape by using the function f(x) described above.
  • a rolling molding for example, a workpiece is held between a pair of rolling dies rotating in the same direction and the tooth part of the rolling die is transferred as a groove to the outer peripheral surface of the workpiece, whereby it is possible to manufacture a gear having a tooth profile of a predetermined shape.

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  • Engineering & Computer Science (AREA)
  • General Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Business, Economics & Management (AREA)
  • Theoretical Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Human Resources & Organizations (AREA)
  • Mechanical Engineering (AREA)
  • Geometry (AREA)
  • Strategic Management (AREA)
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  • Marketing (AREA)
  • Evolutionary Computation (AREA)
  • Entrepreneurship & Innovation (AREA)
  • Computer Hardware Design (AREA)
  • General Business, Economics & Management (AREA)
  • Mathematical Optimization (AREA)
  • Educational Administration (AREA)
  • Primary Health Care (AREA)
  • Manufacturing & Machinery (AREA)
  • Mathematical Analysis (AREA)
  • General Health & Medical Sciences (AREA)
  • Development Economics (AREA)
  • Pure & Applied Mathematics (AREA)
  • Health & Medical Sciences (AREA)
  • Game Theory and Decision Science (AREA)
  • Operations Research (AREA)
  • Quality & Reliability (AREA)
  • Computational Mathematics (AREA)
  • Gears, Cams (AREA)
US17/345,748 2020-07-13 2021-06-11 Method for manufacturing gear Abandoned US20220009044A1 (en)

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
JP2020-119938 2020-07-13
JP2020119938A JP2022024253A (ja) 2020-07-13 2020-07-13 歯車の製造方法

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JP (1) JP2022024253A (zh)
CN (1) CN113935120A (zh)
DE (1) DE102021116682A1 (zh)

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US1895360A (en) * 1930-02-17 1933-01-24 Wildhaber Ernest Gearing
US20110083523A1 (en) * 2009-10-09 2011-04-14 Chin-Lung Huang Gear and method for forming tooth profile thereof
US20140193195A1 (en) * 2011-06-24 2014-07-10 Sms Siemag Ag Toothing for operation at a deflection angle and production method

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US1895360A (en) * 1930-02-17 1933-01-24 Wildhaber Ernest Gearing
US20110083523A1 (en) * 2009-10-09 2011-04-14 Chin-Lung Huang Gear and method for forming tooth profile thereof
US20140193195A1 (en) * 2011-06-24 2014-07-10 Sms Siemag Ag Toothing for operation at a deflection angle and production method

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DE102021116682A1 (de) 2022-01-13
JP2022024253A (ja) 2022-02-09
CN113935120A (zh) 2022-01-14

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